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For the leveling circuit in Figure B-1

 Figure B-1 Level Circuit

and these observed elevation differences

 Obs Line dElev Obs Line dElev 1 BMA-Q +8.91 5 BMA-R -3.56 2 BMB-Q -2.92 -- -- 3 BMC-Q -4.67 6 BMC-R -17.12 4 BMD-Q -8.66 7 BMD-R -21.10

what are the elevations of points Q and R?

A traditional simple adjustment is difficult to apply in this situation. Because point Q is connected to four benchmarks and point R to three, any simple adjustment attempted will result in multiple elevations for each point.

With a small network like this, a Brute Force approach might be feasible. Using the observed elevation differences, compute all possible elevations for points Q and R, then simply average them.

Point Q elevations and their average are:

Similarly, for point R:

Compute So

Compute residuals using the adjusted elevations and the individually computed elevations used for the averages.
 v = MPVQ-ElevQ v2 sums -0.015 0.000225 +0.015 0.000225 -0.035 0.001225 +0.035 0.001225 0.002900 v = MPVR-ElevR v2 +0.007 0.000049 -0.033 0.001089 +0.027 0.000729 0.001867 0.004767
There are seven observations (m) and two unknown elevations (n).